Johannes Mehserle said in the handwritten letter that he "never intended" to shoot 22-year-old Oscar Grant, who died of a gunshot wound to the back after being pulled off a Bay Area Rapid Transit train on New Year's Day 2009.
The emotional letter is dated July 4, four days before a Los Angeles jury convicted him of involuntary manslaughter.
"For now, and forever I will live, breathe, sleep, and not sleep with the memory of Mr. Grant screaming "You shot me" and putting my hands on the bullet wound thinking the pressure would help while I kept telling him "You'll be okay!" Mehserle said in the letter, released by attorney Michael Rains.
Thursday's verdict outraged Grant's family and touched off violent protest in Oakland, where the case has enflamed racial tensions.
Mehserle, 28, testified during his trial that he struggled with Grant and saw him digging in his pocket as officers responded to reports of a fight at a train station.
Fearing Grant may have a weapon, Mehserle said he decided to shock Grant with his Taser but pulled his .40-caliber handgun instead. Grant was shot as he lay face-down.
The jury found that Mehserle didn't mean to kill Grant, but that his behavior was still so negligent that it was criminal.
Mehserle's letter made no mention of his intention to pull a Taser. He also said he had wanted to communicate with Grant's family in the days after the shooting but was prevented by death threats to him and his family and friends.
"I have and will continue to live everyday of my life knowing that Mr. Grant should not have been shot," he wrote. "It saddens me knowing that my actions cost Mr. Grant his life, no words express how truly sorry I am."